THE LONG RUN RELATIONSHIP BETWEEN SAVING AND INVESTMENT IN INDIA

Transcription

1 THE LONG RUN RELATIONSHIP BETWEEN SAVING AND INVESTMENT IN INDIA Dipendra Sinha Department of Economics Macquarie University Sydney, NSW 2109 AUSTRALIA and Tapen Sinha Center for Statistical Applications Instituto Techonologico Autonomo de Mexico Mexico, D. F. MEXICO

2 Abstract In the long run, the present value of current account balance would not get indefinitely large without precipitating in a macroeconomic crisis. This simple insight produces an econometrically testable relationship between saving and investment. We develop and test a variant of such a testable hypothesis for India using the recent cointegration methodology. The results indicate that there exists a positive long run relationship between saving and investment in India. This convergence implies that India is unlikely to suffer macroeconomic instability like countries such as Mexico in the long run. JEL Codes: C32, E20, O11 2

3 Introduction In the past sixteen years, economists have been studying the relationship between saving and investment with renewed vigor. The biggest impetus comes from Feldstein and Horioka (1980). The main focus of the literature following Feldstein and Horioka is international capital mobility in the industrialized countries. With more sophisticated econometric methodology and more data availability for other countries, we are beginning to understand the relationship between saving and investment better. We are also recognizing the implications of the presence or absence of close relationships between saving and investment. In this paper, we develop a model which produces a clearly econometrically testable hypothesis: saving and investment should be cointegrated. We test this theory for India. During the last few years, the saving rate in India has fallen marginally raising concern that it might adversely affect economic growth. We take a long run view. We explore whether there is a long run relationship between saving and investment which is crucial for macroeconomic stability. A Dynamic Stochastic Model of Saving and Investment Suppose that there are n countries in the world each of them small enough not to affect the world interest rate (R) individually. We will use subscript t to denote time and subscript i to denote a country. We formulate a variant of the linearized version of the model proposed by Feldstein (1983) which is used by Coakley et al (1995): S it = a k + S it-1 + b k R t + e kit (1) 3

4 Equation (1) summarizes the stylized facts that saving (S) is a process with unit root and that saving at time t for country i (S it ) depends positively on (real) world interest rate (R) at time t. I it = a l + I it-1 - b l R t +e lit (2) Equation (2) encapsulates the stylized facts that investment (I) is also a unit root process but has a negative relation with interest rate. More generally, I it = a l + I it-1 - b l R t + d(s it-1 - I it-1 ) +e lit (2 / ) The additional term d(s it-1 - I it-1 ) is an error correction term to reflect a risk premium. The terms e kit and e lit are iid white noise processes and a k, b k, a l, b l and d are constants. Two equations (1) and (2 / ) (or, (1) and (2) as (2 / ) becomes identical to (2) if d = 0) can be used to solve for R t : Subtracting (2 / ) from (1), we get S it - I it = a k - a l + S it-1 - I it-1 + (b k - b l )R t - d(s it-1 - I it-1 ) + e kit - e lit (3) If it is a closed system with n countries, then total saving in each period must be equal to the total investment in that period. This means ΣS it = ΣI it summing over i. Summing over i in equation (3), we get, 0 = n(a k - a l ) + n(b k - b l )R t + Σ(e kit - e lit ) (4) Thus, assuming b k b l, we solve for R t from (4) by noting that differences of independence white noise processes still produce white noise (say, z t ): R t = [a l - a k + Σ(e kit - e lit )/n]/(b k - b l )= R* + z t (5) Let C it = S it - I it. Then, from equation (3) we get by substituting the expression (5), 4

5 C it = C it-1 - d(c it-1 ) + (b k + b l )z t + (e kit - e lit ) (6) We can take expectations in (6) on both sides conditional on time t-1 to get E t-1 (C it ) = C it-1 - d(c it-1 ) (7) For a country i, the present value of the conditional expectations of C it must be bounded above: E t-1 (Σ C it /(1 + R*) t ) < (8) Given (7), (8) follows provided (1-d)/(1+R*) < 1. In fact, we can show by simple algebra that E t-1 (Σ C it /(1 + R*) t ) = C it-1 (1-d)(1+R*)/(R*+d) (9) provided (1-d)/(1+R*) < 1. This solvency condition for the country shows that in the long run, the only credible path of saving and investment should be such that they are cointegrated. Otherwise (9) does not hold. Moreover, the cointegrating vector should be (1, -1) because C it = S it - I it by definition. Any other relation would not be viable in the long run. Thus, the model actually produces a testable hypothesis. However, since our model rests on a number of restrictive assumptions (such as a closed system assumption and a small country assumption), the empirical results may not exactly produce a cointegrating vector (1, -1). The other implication of the model is the relation between import and export. If, the central bank activities are ignored (and in the long run, the central bank cannot continue to buy or sell securities without a credibility constraint), the capital account is the flip side of net export. Hence, in the long run, export and import should be cointegrated with a cointegrating vector of (1, -1) as well. 5

6 What Can We Say About Cross Section Correlation Between Saving and Investment? Feldstein and Horioka (1980) upset conventional wisdom by proclaiming that a high saving investment correlation in pooled cross section data of a number of (industrialized) countries imply capital immobility among them. This assertion holds under very restrictive theoretical conditions (see Frankel (1992)). Moreover, simulations with artificial economies have shown that high saving and investment correlation can persist even with perfect capital mobility (Baxter and Crucini (1993) and Finn (1991)). We deliberately refrain from drawing any conclusion based on pooled cross section analysis of our dataset for the following reason: All the basic series exhibit unit roots. Gonzalo (1994) has shown that in the presence of unit roots in the time series data, none of the usual test statistics for the ordinary least square regressions have standard distributions. Hence, any inference drawn from them are very likely to be erroneous even with very large samples. Therefore, applying their argument in these data series seem entirely inappropriate. Data and Methodology The data are from the Penn World Table and it is for the period Penn World Table data which were developed by the International Comparison Project in cooperation with the World Bank are reportedly more reliable than data from other sources. The data are being constantly updated. We use the most 6

7 recent version of the Penn World Table (version 5.6). The data series are described in detail in Summers and Heston (1991). The two variables considered are gross domestic saving and gross domestic investment as percentages of gross domestic product. We call these variables SR and IR respectively. We use the Phillips-Perron (1988) unit root test. The test is well suited for analyzing time series whose differences may follow mixed ARMA (p,q) processes of unknown order in that the test statistic incorporates a nonparametric allowance for serial correlation. Consider the following equation: y t = c ~ 0 + c ~ 1 y t-1 + c ~ 2 (t - T/2) + ν t (10) where {y t } is the relevant time series in equation (10), T is the number of observations and ν t is the error term. The null hypothesis of a unit root is H 0 : c ~ 1 =1. We can drop the trend term to test the stationarity of a variable without the trend. The concept of cointegration is proposed by Granger (1981). Engle and Granger (1987) provide an axiomatic foundation of the methodology. Two (or more) I(1) variables are said to be cointegrated if there exists a linear combination of them that is stationary. We use the Johansen-Juselius (see Johansen (1988) and Johansen and Juselius (1990) for details) tests for cointegration. The method can be shown to have the error correction representation of the VAR(p) model with Gaussian errors: Z t = a 0 + Γ 1 Z t-1 + Γ 2 Z t Γ p-1 Z t-p+1 + ΠZ t-p + BX t + u t (11) where Z t is a an mx1 vector of I(1) variables, X t is an sx1 vector of I(0) variables, Γ 1, Γ 2, Γ p-1, Π are mxm matrices of unknown parameters, B is an mxs matrix and 7

8 u t N(0, Σ). The maximum likelihood method is used to estimate (11) subject to the hypothesis that Π has a reduced rank, r < m. The hypothesis, therefore, is as follows: H(r): Π = αβ / (12) where α and β are m x r matrices. If certain conditions are fulfilled, equation (12) implies that the process Z t is stationary, Z t is non-stationary, and that βz t is stationary. βz t are known as the cointegrating relations and β the cointegrating vector. In our model C t plays the role of Z t in (11). If we find that SR and IR are cointegrated, the relevant hypothesis for the vector β to be tested is H 0 : β / = (1, -1). Results The results of the Phillips-Perron unit root tests on the levels and first differences of the variables are in table 1. The results indicate that both SR and IR are non-stationary in their level form but stationary in their first difference form. Thus, we proceed with the cointegration tests. The results of the maximal eigenvalue and trace tests are in tables 2 and 3 respectively. The results [Tables 1-3 about here] of both the maximal eigenvalue and trace tests indicate that there is one cointegrating vector. Thus, our results are quite robust. The normalized coefficients (we normalize the vector with respect to SR) for β are and (for SR and IR respectively). Thus, we see that the coefficients of the vector are fairly close to (-1, 1). Next, we test the null hypothesis that β / is 8

9 (1, -1). The test statistic (the likelihood ratio) has a χ 2 distribution with one degree of freedom. The test statistic is and the p-value is.014 which indicates that we cannot reject the null hypothesis that β / is (1, -1) at the 5% level of significance. Thus, for India the strict condition of cointegrated saving and investment with the cointegrating vector (1, -1) cannot be rejected. Thus, the empirical results provide full support for our model. Conclusions In this paper, we develop and empirically test a variant of the Feldstein- Horioka hypothesis of saving-investment using data for India. First, we test for unit roots. We find that both saving and investment rates are non-stationary in their levels but stationary in their first differences. This gives us a high degree of confidence on the equations (1) and (2) that incorporate the stylized facts. Next, we proceed with the cointegration tests using the Johansen-Juselius framework. The results show that saving and investment ratios have a long run relationship for India. Our tests also show that we cannot reject the null hypothesis of a one-toone correspondence between saving rate and investment rate. This convergence implies that if past data are any guide, India is unlikely to suffer from macroeconomic instability in the long run. 9

10 References Baxter, Marianne and Crucini, Michael J. (1993) Explaining Saving-Investment Correlations, American Economic Review, Vol. 83, Coakley, Jerry, Kulasi, Farida and Smith, Ron. (1995) Current Account Solvency and Feldstein Horioka Puzzle, Birbeck College Discussion Paper No. 8/95. Engle, Robert F. and Granger, Clive W. J. (1987) "Cointegration and Error Correction: Representation, Estimation, and Testing", Econometrica, Vol. 55, Feldstein, Martin (1983) Domestic Saving and International Capital Movements in the Long Run and in the Short Run, European Economic Review, Vol. 21, Feldstein, Martin and Horioka, Charles (1980) Domestic Saving and International Capital Flows, Economic Journal, Vol. 90, Finn, Mary G. (1991) On Savings and Investment Dynamics in a Small Open Economy, Journal of International Economics, Vol. 29, Frankel, Jeffrey (1992) Measuring International Capital Mobility: A Review, American Economic Review. Vol. 82, Gonzalo, Jesus (1994) Cointegration and Aggregation, Unpublished Working Paper, Boston University. Granger, Clive W. J. (1981) Some Properties of Time Series Data and Their Use in Econometric Model Specification, Journal of Econometrics, Vol. 16, Johansen, Soren (1988) Statistical Analysis of Cointegration Vectors, Journal of Economic Dynamics and Control, Vol. 12, Johansen, Soren and Juselius, Katarina (1990) The Maximum Likelihood Estimation and Inference on Cointegration -- with Application to Demand for Money, Oxford Bulletin of Economics and Statistics, Vol. 52, Mackinnon, James G. Critical Values for Cointegration, in Long -run Economic Relationships: Readings in Cointegration (Ed.) Robert F. Engle and Clive W. J. Granger, Oxford: Oxford University Press, Osterwald-Lenum, Michael (1992) A Note with Fractiles of the Asymptotic Distribution of the Likelihood Rank Statistics: Four Cases, Oxford Bulletin of Economics and Statistics, Vol. 54,

11 Phillips, Peter C. B. and Perron, Pierre (1988) "Time Series Regression with a Unit Root," Biometrika, Vol. 75, Schwert, G. William (1989) Test for Unit Roots: A Monte Carlo Investigation, Journal of Business and Economic Statistics, Vol. 7, Summers, Robert and Heston, Alan (1991) The Penn World Table (Mark 5): An Expanded Set of International Comparisons, , Quarterly Journal of Economics, Vol. 106,

12 Table 1. Phillips-Perron Unit Root Tests for Levels of Savings Ratios and Investment Ratios Level First Difference Test Statistic Critical Value Test Statistic Critical Value SR IR Note: The critical values at the 5% level are from Mackinnon (1991). The lag of 3 was determined using the Schwert (1989) Criterion. Table 2. Maximal Eigenvalue Tests for Cointegration Between Saving and Investment Null Alternative Test Statistic Critical Value Hypothesis Hypothesis r=0 r= r<=1 r= Note: The critical values from Osterwald-Lenum (1992) are for the 95% quantile. Table 3. Trace Tests for Cointegration Between Saving and Investment Null Alternative Test Statistic Critical Value Hypothesis Hypothesis r=0 r= r<=1 r= Note: The critical values from Osterwald-Lenum (1992) are for the 95% quantile. 12